# cdfBinomial#

## Purpose#

Computes the binomial cumulative distribution function.

## Format#

p = cdfBinomial(successes, trials, prob)#
Parameters:
• successes (NxK matrix, Nx1 vector or scalar) – Must be a positive number and must be less than trials

• trials (LxM matrix) – ExE conformable with successes. trials must be greater than successes.

• prob (PxQ matrix) – ExE conformable with successes. The probability of success on any given trial with successes $$0 < prob < 1$$.

Returns:

p (NxK matrix, Nx1 vector or scalar) – Each element in p is the binomial cdf value evaluated at the corresponding element in x.

## Examples#

What are the chances that a baseball player with a long-term batting average of .317 could break Ichiro Suzuki’s record of 270 hits in a season if he had as many at bats as Ichiro had that year, 704?

/*
** We will find the cumulative probability
** of our player getting 270 or
** fewer hits in the season
*/

// Number of successes
successes = 270;

// Number of trials
trials = 704;

// Probability of success
prob = 0.317;

// Call cdfBinomial
p = cdfBinomial(successes, trials, prob);
p = 0.9999199430052614


Therefore the odds of this player breaking Ichiro’s record:

1-p = 0.0000000000037863 or 0.0000000003786305%


## Remarks#

$\begin{split}\mathit{\mathrm{\mathtt{P\left( x\, \leq k \right)}} =}\mathit{\sum\limits_{i = 0}^{k}\begin{pmatrix} n \\ i \\ \end{pmatrix}\, p^{i}\left( 1 - p \right)^{n - i}}\end{split}$

For invalid inputs, cdfBinomial() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr() will return a 2; etc.